Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations
Raymond, Dominic *
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
Skwame, Yusuf
Department of Mathematical Science, Adamawa State University, Mubi, Nigeria.
Adiku, Lydia
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.
Keywords: Four-step, hybrid point, fourth derivative, power series, ODE’s, interpolation